In reply to Rick Wicklin.

Thank you for taking the time to think aobut my question. You confirm my own instinct, it depends on the application.
The subject comes up in finance, for example with the application of mean-variance portfolio theory in constructing an "efficient frontier". See, for example:
http://epublications.bond.edu.au/cgi/viewcontent.cgi?article=1078&context=ejsie
The same portfolio covariance matrix in that application, containing some negative price-change (return) covariance (which does occur in practice, and often results in a non PD matrix) leads to my question with respect to the MD^2.